Geoffrey Chase, a mechanical engineer at the University of Canterbury, responded.

There are a variety of reasons a refrigerator hums. The source is typically
a vibration from the machinery or an interaction between machinery and
refrigerants, creating motion in the air which is sound. There are therefore
several possible causes for these sounds.

The pump used to pump the (cool) refrigerant through the fridge or move
air in the fridge, and the pump used to cool this liquid is one possibility.
Pumps are essentially motors with rotating parts which can vibrate if not made
precisely round. Hence, cheaper manufacture of these parts may be one
reason.

Sound is tranmitted quite well through some materials and air and is
blocked by others, called sound insulators. So another possible cause is when sound
insulation is skimped on in order to save money and/or weight.

Refrigerators today are typically bigger than older ones. These require
the pumps to work harder and hence their hum tends to be louder. The same
effect can be caused by keeping the inside of your refrigerator colder or
having more things inside it. Each requires more effort and fridges today tend to
be kept colder and more filled than in past.

Pumping at higher pressures can also cause the tubes that the refrigerant
fluid flows through to vibrate. This is particularly so if cheaper, more
flexible, plastic tubing is used, instead of steel tubing, in order to
save cost and weight. Additionally, bigger fridges may well have
longer tubing, as well as more of it, given that modern fridges try to keep
the inside cold as evenly as possible in contrast to older models.

Those are some possible causes, all centered on vibration combined with
cheaper materials and lower quality of manufacture, as well as those changes
brought about by consumer demand for different features and better performance.